\chapter{Introduction}
\section{Motivation}
Combustion is a complex process requiring knowledge from a variety of different fields such as thermodynamics, fluid dynamics, chemistry, turbulence, heat and mass transfer. In recent years a lot of effort has been put into increasing the energy efficiency of combustion. The efforts have been mostly focused on increasing the efficiency with regard to the First Law of Thermodynamics Eq. \ref{eq:1st law}, but some aspects of combustion (like flame stability) are believed to be controlled by the Second Law of Thermodynamics Eq. \ref{eq:2nd law} therefore further investigation is needed on this subject.

Exergy analysis of combustion has traditionally only been done at a bulk scale, looking at the difference in flow exergy at the input and output streams. This ``black box'' approach has limited usefulness, as it does not give any information how the irreversibilities arise. A local study of entropy production in a flame can improve our understanding of several combustion phenomena. 

Irreversible thermodynamics, turbulent flow and combustion are very complex research fields. This thesis seeks to include theories from these three topics in modelling the local entropy production of a jet diffusion flame.

The current design of combustors is largely based on empirical relations with trial and error in order to find an optimal operating window. In recent years many new fuels have been introduced as possible energy carriers, and it is too time consuming to test these fuels thoroghly for all operating parameters one might encounter. 

\section{Problem description}
Exergy is a measure of the maximum useful work from a thermodynamic process. Irreversibility is synonymous with the term exergy destruction, which is the amount of the useful work that is lost in a process. The thermodynamic irreversibility of a process is characterized its entropy generation (from Eq. \ref{eq:2nd law}) in the process. For continuous processes performed by a system, Eq.\ref{eq:Gouy-Stodola}, gives the relation between the rate of exergy destruction $\dot{I}$, and $\dot{S}_{gen}$ is the rate of entropy generation.

\begin{equation}
\dot{I}=T_0 \dot{S}_{gen}
\label{eq:Gouy-Stodola}
\end{equation}

From Som(2005) \cite{Som2005} the exergetic efficiency or second law efficiency is then given as

\begin{equation}
\eta_{II}=1-\frac{\dot{I}}{\dot{A}_{in}},
\label{eq:Second law efficiency}
\end{equation}

where $\dot{A}_{in}$ represents the exergy flowing in to the system.

The irreversibility of heat transfer, mass transfer and chemical reaction in a turbulent nonpremixed hydrogen jet flame have been computed from a relatively simple model coupled with experimental data. The author has written a routine using prescribed probability density functions to solve the flow field. This eliminates the need for an elaborate turbulence model. The resolution of the entropy production calculations was limited by the number of measuring points in the experiment.

